Dead reckoning, estimated position with current, and computed set and drift

# Dead reckoning, estimated position with current, and computed set and drift `input.json` (synthetic, not for navigation): `start` [lat, lon] in decimal degrees, `legs` (each `course` degrees true, `speed_kn` through the water, `minutes`), a forecast `current` (`set` = direction it flows TOWARD, degrees true; `drift_kn`), and a GPS `fix` [lat, lon] at the end of the last leg. Write `solve.py` (Python 3 standard library only); `python solve.py input.json answer.json` writes `answer.json` and `track.svg`. Fresh inputs are used too. ## Rules (plane sailing, 1 minute of latitude = 1 nm) 1. A move of n nm north and e nm east from (lat, lon): dlat = n / 60; mid = lat + dlat / 2; new lat = lat + dlat; new lon = lon + e / (60 * cos(mid)). 2. **DR**: per leg, distance = speed * hours along the course. **EP**: per leg, add the current vector (drift * hours toward set) to the leg's water vector, then move once. 3. Difference from point A to point B: north = (latB - latA) * 60, east = (lonB - lonA) * 60 * cos((latA + latB) / 2). 4. **Set/drift**: vector from the final DR position to the fix; set = atan2(east, north) in degrees mod 360; drift = length / total hours. `ep_error_nm` = distance from the final EP to the fix. **CMG/SMG**: same from `start` to the fix. 5. Round positions to 5 decimals, hours to 4, angles to 1, speeds and distances to 3. `dr` and `ep` list the start and the position after every leg. ## Visual output: track.svg Static, self-contained SVG (root `<svg>`, no scripts, images, links or external assets; renders headless) with `<polyline id="dr-track">`, `<polyline id="ep-track">` and `<circle id="fix">`. The drawing itself is not graded. ## answer.json `{"dr": [[lat, lon], ...], "ep": [...], "hours", "set_deg", "drift_kn", "ep_error_nm", "cmg_deg", "smg_kn"}` ## Scoring Hidden checks (partial credit; all must pass): `dr_positions`, `ep_positions`, `set_and_drift`, `course_speed_made_good`, `track_svg_static` (track.svg exists, follows the static rules, has the ids/tags above), `fresh_run_1`, `fresh_run_2`. Positions within 2e-5 degrees, angles within 0.11, speeds and distances within 0.002. 60-second limit per run.